1.3 Evaluating Limits Analytically 59
1.3 Evaluating Limits Analytically
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the limit.
a.
b.
c.
d.
e.
____ 2. Find the limit.
a.
b.
c.
3
22
d.
3
7
e.
3
10
____ 3. Find the limit.
a.
b.
c. –3
d.
e.
60 Chapter 1: Limits and Their Properties
____ 4. Let and . Find the limit.
a. 2
b.
c. 8
d. –8
e.
____ 5. Let and . Find the limit.
a.
6
b.
14
c.
11
d.
10
e.
2
____ 6. Let and . Find the limits.
a.
b.
c. –
d.
e.
____ 7. Find the limit.
a.
b.
c.
d.
e.
1.3 Evaluating Limits Analytically 61
____ 8. Find the limit.
a.
b.
c.
d.
e. 0
____ 9. Find the limit.
a.
b.
c.
d.
e.
____ 10. Find the limit.
a.
b.
c.
d.
e.
62 Chapter 1: Limits and Their Properties
____ 11. Suppose that and . Find the following limit.
a.
b. –10
c. –3
d. –23
e.
____ 12. Suppose that and . Find the following limit.
a. –11
b. –8
c. 33
d. –14
e.
____ 13. Suppose that and . Find the following limit.
a. 10
b. –5
c. –25
d. –15
e. 150
____ 14. Suppose that and . Find the following limit.
a. 21
b.
c. –21
d.
e.
1.3 Evaluating Limits Analytically 63
____ 15. Suppose that . Find the following limit.
a. 2
b. 125
c. 8
d. 0
e. 15
____ 16. Suppose that . Find the following limit.
a. –5
b. 15
c. –15
d.
e. 3
____ 17. Find the following limit (if it exists). Write a simpler function that agrees with the
given function at all but one point.
a. 40
b. –24
c. 24
d. –40
e.
____ 18. Find the limit (if it exists).
a.
b.
c. –32
d. –8
e.
64 Chapter 1: Limits and Their Properties
____ 19. Find the limit (if it exists).
a. 6
b.
c.
d.
e. .
____ 20. Find the limit (if it exists).
a.
b.
c.
d.
e.
____ 21. Determine the limit (if it exists).
a. 6
b. 48
c. 10
d. 24
e.
____ 22. Determine the limit (if it exists).
a. 8
b.
c.
d. 2
e.
1.3 Evaluating Limits Analytically 65
____ 23. Determine the limit (if it exists).
a. 1
b. 0
c.
d.
e.
____ 24. Find where .
a. 1
b. 4
c. –3
d. 0
e.
66 Chapter 1: Limits and Their Properties
1.3 Evaluating Limits Analytically
Answer Section
1.3 Evaluating Limits Analytically 67